diff --git a/examples/demo_custom_jax_workflow.py b/examples/demo_custom_jax_workflow.py
index c5651942b..204173e0f 100644
--- a/examples/demo_custom_jax_workflow.py
+++ b/examples/demo_custom_jax_workflow.py
@@ -58,20 +58,19 @@ def loss_fn(y_true, y_pred):
 
 model = MyModel(hidden_dim=256, output_dim=4)
 
-optimizer = optimizers.SGD(learning_rate=0.0001)
+optimizer = optimizers.SGD(learning_rate=0.001)
 dataset = Dataset()
 
-
-######### Custom JAX workflow ###############
-
-
 # Build model
-x = ops.convert_to_tensor(np.random.random((1, 128)))
+x = np.random.random((1, 128))
 model(x)
 # Build optimizer
 optimizer.build(model.trainable_variables)
 
 
+######### Custom JAX workflow ###############
+
+
 def compute_loss_and_updates(
     trainable_variables, non_trainable_variables, x, y
 ):
diff --git a/examples/demo_custom_layer_backend_agnostic.py b/examples/demo_custom_layer_backend_agnostic.py
index 924fc25ec..8083dbcac 100644
--- a/examples/demo_custom_layer_backend_agnostic.py
+++ b/examples/demo_custom_layer_backend_agnostic.py
@@ -1,5 +1,6 @@
 import numpy as np
 
+import keras_core
 from keras_core import Model
 from keras_core import backend
 from keras_core import initializers
@@ -42,11 +43,11 @@ class MyDropout(layers.Layer):
         # Use seed_generator for managing RNG state.
         # It is a state element and its seed variable is
         # tracked as part of `layer.variables`.
-        self.seed_generator = backend.random.SeedGenerator(1337)
+        self.seed_generator = keras_core.random.SeedGenerator(1337)
 
     def call(self, inputs):
-        # Use `backend.random` for random ops.
-        return backend.random.dropout(
+        # Use `keras_core.random` for random ops.
+        return keras_core.random.dropout(
             inputs, self.rate, seed=self.seed_generator
         )
 
diff --git a/examples/demo_functional.py b/examples/demo_functional.py
index 04a733fb5..ba607fd0c 100644
--- a/examples/demo_functional.py
+++ b/examples/demo_functional.py
@@ -8,8 +8,10 @@ from keras_core import optimizers
 
 inputs = layers.Input((100,), batch_size=32)
 x = layers.Dense(256, activation="relu")(inputs)
+residual = x
 x = layers.Dense(256, activation="relu")(x)
 x = layers.Dense(256, activation="relu")(x)
+x += residual
 outputs = layers.Dense(16)(x)
 model = Model(inputs, outputs)
 
@@ -21,9 +23,9 @@ batch_size = 32
 epochs = 5
 
 model.compile(
-    optimizer=optimizers.SGD(learning_rate=0.001),
+    optimizer=optimizers.Adam(learning_rate=0.001),
     loss=losses.MeanSquaredError(),
-    metrics=[metrics.MeanSquaredError()],
+    metrics=[metrics.CategoricalAccuracy(name="acc"), metrics.MeanSquaredError(name="mse")],
 )
 history = model.fit(
     x, y, batch_size=batch_size, epochs=epochs, validation_split=0.2